The BCD adder to add two decimal digits needs minimum of

Key idea: Add two 4-bit BCD digits using a 4-bit binary adder; if the raw sum is greater than 9 or there is an outgoing carry, add 6 (binary 0110) as a correction.

• Initial 4-bit addition: Use a 4-bit binary ripple-carry adder to add the two BCD digits. This requires 4 full adders.

• Correction (add 6 = 0110) when needed: Implement the addition of 0110 to the 4-bit raw sum with minimal extra adders by examining each bit:

  • Least significant bit (bit 0): adding 0 changes nothing — no adder required.

  • Bit 1: add 1 to the raw sum bit; with no incoming carry to this position from bit 0, this can be done with a half adder.

  • Bit 2: add 1 plus any carry generated from bit 1; this needs a full adder.

  • Bit 3: add 0 plus any carry from bit 2; this is a half adder (adding the carry to the single bit).

Total minimal adder count: 4 full adders for the initial 4-bit addition, plus 1 additional full adder and 2 half adders for the correction, giving 5 full adders and 2 half adders.